Abstract: A signed distance field (SDF) is a widely used geometric representation for robust collision detection between complex geometries, which is crucial for contact-rich simulations. While numerous works have studied SDF representations and SDF-based collision detection, achieving both memory efficiency and high accuracy while maintaining scalability remains a challenge. In this paper, we propose a novel SDF representation, Tetra-Encoded SDF (TE-SDF), which combines the adaptive spatial discretization of a tetrahedral mesh with exact-distance evaluation localized to each tetrahedron by encoding a compact set of candidate surface faces per tetrahedron. We demonstrate the effectiveness of TE-SDF in contact-rich simulation by implementing a fully GPU-accelerated collision detector based on TE-SDF and integrating it into a GPU-accelerated simulation framework. Our results show that TE-SDF enables memory-efficient, accurate, and scalable collision detection, expanding the domain of robotic simulation scenarios that can be handled in practice.